If A's income is 25% more than B's and B's income is 20% more than C's, by what percent is A's income more than C's?

Question

Accepted Answer

To determine by what percent A's income is more than C's, we need to follow the given relationships between their incomes.

1. **Understanding the Relationships:**
   - A's income is 25% more than B's.
   - B's income is 20% more than C's.

2. **Calculating B's Income in Terms of C's:**
   - Let's assume C's income is $ C $.
   - B's income is 20% more than C's, so B's income is $ B = C + 0.2C = 1.2C $.

3. **Calculating A's Income in Terms of B's:**
   - A's income is 25% more than B's, so A's income is $ A = B + 0.25B = 1.25B $.

4. **Substituting B's Income in Terms of C's into A's Income:**
   - Substitute $ B = 1.2C $ into $ A = 1.25B $:
   - $ A = 1.25 \times 1.2C = 1.5C $.

5. **Determining the Percentage Increase from C to A:**
   - A's income is $ 1.5C $, and C's income is $ C $.
   - The increase in income from C to A is $ 1.5C - C = 0.5C $.
   - The percentage increase is $ \frac{0.5C}{C} \times 100\% = 50\% $.

Therefore, A's income is 50% more than C's income, which corresponds to Option 4.

**Explanation for Incorrect Options:**

- **Option 1 (0.15 or 15%):** This option suggests that A's income is only 15% more than C's, which is incorrect because the calculations show a 50% increase.
  
- **Option 2 (0.25 or 25%):** This option suggests a 25% increase, which is incorrect as the calculations clearly indicate a 50% increase from C to A.
  
- **Option 3 (0.33 or 33%):** This option suggests a 33% increase, which is also incorrect. The correct calculation shows a 50% increase.

In conclusion, the correct answer is Option 4, as A's income is indeed 50% more than C's income.